Local unitary representations of the braid group and their applications to quantum computing
Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2016
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oai:scielo:S0034-742620160002000062017-04-17Local unitary representations of the braid group and their applications to quantum computingDelaney,ColleenRowell,Eric CWang,Zhenghan topological quantum computation braid group representations localizations quantum algebra Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.50 n.2 20162016-12-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262016000200006en10.15446/recolma.v50n2.62211 |
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Delaney,Colleen Rowell,Eric C Wang,Zhenghan |
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Delaney,Colleen Rowell,Eric C Wang,Zhenghan Local unitary representations of the braid group and their applications to quantum computing |
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Delaney,Colleen Rowell,Eric C Wang,Zhenghan |
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Delaney,Colleen |
title |
Local unitary representations of the braid group and their applications to quantum computing |
title_short |
Local unitary representations of the braid group and their applications to quantum computing |
title_full |
Local unitary representations of the braid group and their applications to quantum computing |
title_fullStr |
Local unitary representations of the braid group and their applications to quantum computing |
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Local unitary representations of the braid group and their applications to quantum computing |
title_sort |
local unitary representations of the braid group and their applications to quantum computing |
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Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations. |
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas |
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2016 |
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http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262016000200006 |
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AT delaneycolleen localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing AT rowellericc localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing AT wangzhenghan localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing |
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